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2 years ago

I dont understand the circled question ....please help!

Mathematics

1 answer:

irina1246 [14]2 years ago

7 0

Parallel lines NEVER intersect/meet, this is because they have the same slope and they go in the same direction.

These lines are parallel because they have the same slopes of 3/4 (because they go 3 units up and 4 units to the right. slope = rise/run)

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Work out an expression, in terms of x, for the perimeter of the shape. Simplify your answer.

sammy [17]

Answer:1+3x+9+x+8+2x= 6x+9

so =3(x+3)

Step-by-step explanation:

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2 years ago

The graphs of the polar curves r = 4 and r = 3 + 2cosθ are shown in the figure above. The curves intersect at θ = π/3 and θ = 5π

Gennadij [26K]

(a)

$\displaystyle \frac{1}{2} \cdot \int_{\frac{\pi}{3}}^{\frac{5\pi}{3}} \left(4^2 - (3 + 2\cos\theta)^2 \right) \, d\theta$

or, via symmetry

$\displaystyle\frac{1}{2} \cdot 2 \int_{\frac{\pi}{3}}^{\pi} \left(4^2 - (3 + 2\cos\theta)^2 \right) \, d\theta$

____________

(b)

By the chain rule:

$\displaystyle \frac{dy}{dx} = \frac{ dy/ d\theta}{ dx/ d\theta}$

For polar coordinates, x = rcosθ and y = rsinθ. Since
r = 3 + 2cosθ, it follows that

$x = (3 + 2\cos\theta) \cos \theta \\ 
y = (3 + 2\cos\theta) \sin \theta$

Differentiating with respect to theta

$\begin{aligned}
\displaystyle \frac{dy}{dx} &= \frac{ dy/ d\theta}{ dx/ d\theta} \\
&= \frac{(3 + 2\cos\theta)(\cos\theta) + (-2\sin\theta)(\sin\theta)}{(3 + 2\cos\theta)(-\sin\theta) + (-2\sin\theta)(\cos\theta)} \\ \\
\left.\frac{dy}{dx}\right_{\theta = \frac{\pi}{2}}
&= 2/3
\end{aligned}$

2/3 is the slope

____________

(c)

"distance between the particle and the origin increases at a constant rate of 3 units per second" implies dr/dt = 3

Angle θ and r are related via r = 3 + 2cosθ, so implicitly differentiating with respect to time

 $\displaystyle\frac{dr}{dt} = -2\sin\theta \frac{d\theta}{dt} \quad \stackrel{\theta = \pi/3}{\implies} \quad 3 = -2\left( \frac{\sqrt{3}}{2}}\right) \frac{d\theta}{dt} \implies \\ \\ \frac{d\theta}{dt} = -\sqrt{3} \text{ radians per second}$

5 0

2 years ago

Hussien says that the lcm of 6 and 4 is the same as the hcf of 36 and 24 is Hussein correct and why

Lapatulllka [165]

Answer:

LCM :

6 x 1 = 6

6 x 2 = 12

6 x 3 = 18

6 x 4 = 24

Meanwhile

4 x 1 = 4

4 x 2 = 8

4 x 3 = 12

4 x 4 = 16

4 x 5 = 20

4 x 6 = 24

The LCM of 6 and 4 is 12

HCF:

36 : 1,2,3,4,6,9,12,36

24 : 1,2,3,4,6,8,12,24

HCF of 36 and 24 is 12

So therefore Hussein is correct because both the LCM and HCF is 12

7 0

2 years ago

Read 2 more answers

the length of a rectangle is twice its width. if the perimeter of the rectangle is 54m find its area

mixer [17]

Answer:

You can denote the width of the rectangle as x,

than the length of the rectangle will be 2x

and the perimeter of the rectangle will be two length plus two width and it should be equal to 54 in

and the equation will look 2(2x)+2x=54

solving the equation 6x=54, x=9in

So the width of the rectangle is 9in and the length is 9*2=18in

and the area of the rectangle is 9*18=162 sq in.

7 0

2 years ago

4 (153) + (6 x 3) - 2

bekas [8.4K]

Answer: 628

Step-by-step explanation:

Multiply the numbers

Add the numbers

7 0

2 years ago